Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 8
Problem 1
Griths 5.22
(a) Construct the completely antisymmetric wave function (xA , xB , xC ) for three identical fermions, one in the state 5 , one in the state 7 , and one in the
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Winter 2014
MIDTERM EXAM SOLUTIONS
CLOSED-Book Problems
(total 40 points)
Problem C1: Angular Momentum Basics (10 pts)
(a) Write down the eigenvalue equation for the total angular momentum operato
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 7
Problem 1
Griths 5.16
The density of copper is 8.96g/cm3 and its atomic weight is 63.5g/mole.
(a) Calculate the Fermi energy for copper (Eq. 5.43). Assume q = 1 and give your
answer
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 1 Solutions
Problem 1
Griths 4.3
Use equations 4.27, 4.28, and 4.32 to construct the spherical harmonics Y00 and Y21 .
Check that they are normalized and orthogonal.
Build Y00 starting
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 2 Solutions
Problem 1
Griths 4.11
(a) Normalize the radial function R20 and construct the wave function 200 .
We require
r 2 r/a 2
c0 2
1
e
r dr
2a
2a
0
0
c0 2 3
z 2 z 2
c2 a
1
a
1
e
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 3 Solutions
Problem 1
Griths 4.18
The raising and lower operators L change the value of ml by one unit,
L flm = Am flm1
l
where Am is some constant. Compute Am , assuming that the eige
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 4 Solutions
Problem 1
Griths 4.34
(a) Apply S to the state |1 0 (Eq. 4.177) and conrm that you get
2|1 1 .
Carefully note that were talking about two particle systems here. In the prob
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 5 Solutions
Problem 1
Griths 5.4
Look at Eq. 5.10 in Griths.
(a) If a and b are orthogonal and normalized, what is the constant A? (Compute, do
not guess.)
Writing out all the terms an
Physics 327: Quantum Mechanics II
Prof. Michael S. Vogeley
Problem Set 6
Problem 1
Griths 5.7
In Eqs. 5.15, 5.16, and 5.17 we found two-particle states for distinguishable particles,
identical bosons, and identical fermions, respectively. Take a look at t